Ask Mr. Smarty Plants

The Lady Bird Johnson Wildflower Center is dedicated to the growth, protection and propagation of plants native not only to North America but to the areas in which those plants are being grown. Albizia julibrissin, Mimosa or Silk Tree, is native to China and therefore out of our range of expertise. Read this article from the Plant Conservation Alliance's Alien Plant Working Group LEAST WANTED on the Mimosa or Silk Tree to learn why we do not recommend it, regardless of what kind of root it has.

You might also be interested in reading this Dave's Garden Forum page on Albizia julibrissin, especially the MANY negative comments. 

There are few trees with a true taproot; they may begin with one, but as time goes by roots will spread from that center root, both in search of water and nutrients and also as a base to stabilize the tree in the ground. From this USDA Forest Service site Mimosa, we extracted these two sentences apropos of your question:

"Breakage: susceptible to breakage either at the crotch due to poor collar formation, or the wood itself is weak and tends to break."

"Roots: surface roots can lift sidewalks or interfere with mowing."

Honestly, most trees will interfere with foundations, sidewalks or driveways if planted too close, regardless of the type of root. Do your research on trees native to your area by going to our Recommended Species, clicking on Texas High Plains on the map, and Narrow Your Search to trees, and indicate the amount of light needed, moisture, etc.  You can follow the plant links to the page on each tree to learn the projected size of that tree. Generally speaking, a tree root system can be from 2 to 4 times the size of the crown of the tree, so consider that when you decide where to plant a tree.